Undergrad Does Lagrangian Mechanics Handle Variable Mass System?

Click For Summary
Lagrangian mechanics can address variable mass systems, unlike Newtonian mechanics, which struggles due to the changing nature of the object's mass. The discussion highlights the challenges in defining an object with variable mass, particularly in relation to Newton's laws, which apply to constant mass systems. Critics argue that without a fixed mass, it becomes complex to formulate the second law of motion. The conversation also points out that many online sources misinterpret the treatment of variable mass systems, emphasizing the importance of accurate information. Understanding these principles is crucial for applications like rocketry, where mass changes significantly during operation.
Pikkugnome
Messages
24
Reaction score
7
How to handle a variable mass system with Lagrangian mechanics? As far as I understand Newtonian mechanics fails, because the object is not constant anymore, it is updated every moment to a new object with different physical properties. I don't immediately see how Lagrangian mechanics can do better.
 
Physics news on Phys.org
What makes you think Newtonian mechanics cannot handle variable mass systems? If that were the case it would be difficult to build a rocket to go to the Moon etc.
 
Reply
  • Like
Likes Vanadium 50 and vanhees71
The first and second law specifically talk about one object. I don't think it is possible to define an object on the fly so to speak as one wishes. What would be the form of the 2nd law, if the object itself was a variable?
 
Pikkugnome said:
The first and second law specifically talk about one object. I don't think it is possible to define an object on the fly so to speak as one wishes. What would be the form of the 2nd law, if the object itself was a variable?
A lot of Internet sources get wrong the treatment of a variable mass system. Not Wikipedia:

https://en.m.wikipedia.org/wiki/Variable-mass_system
 
Reply
  • Informative
  • Like
Likes vanhees71 and berkeman
I have seen several attempts to adapt Lagrangian formalism for variable mass systems. In my opinion all of them failed. Actually I think that there is no satisfactory theory of variable mass systems at all.
 
Last edited:

Thread 'Mousetrap Car Energy efficiency'

For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...
View full post »

Similar threads

Undergrad Checking if a stationary point is a minimum using Lagrangian Mechanics
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
Undergrad Can Any Quantifiable Variable Serve as a Coordinate in Euler-Lagrange Equations?
  • · Replies 5 ·
Replies
5
Views
2K
Insights How to Apply Newton’s Second Law to Variable Mass Systems
  • · Replies 0 ·
Replies
0
Views
2K
Lagrangian Mechanics: Variable Mass System?
  • · Replies 2 ·
Replies
2
Views
2K
Effective Potential in Lagrangian & Hamiltonian Mechanics
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad How Does Landau Justify the Additivity of Lagrangians in Isolated Systems?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Action in Lagrangian Mechanics
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Flaw in Lagrangian Mechanics for a rotary inverted pendulum system? (Simulation vs. Measured)
  • · Replies 11 ·
Replies
11
Views
2K
Motivation for Lagrangian mechanics
  • · Replies 2 ·
Replies
2
Views
2K